Tutorial 10 - Clustering¶

Lecture and Tutorial Learning Goals:¶

After completing this week's lecture and tutorial work, you will be able to:

• Describe a case where clustering would be an appropriate tool, and what insight it would bring from the data.
• Explain the K-means clustering algorithm.
• Interpret the output of a K-means cluster analysis.
• Perform K-means clustering in R
• Visualize the output of K-means clustering in R using a coloured scatter plot
• Identify when it is necessary to scale variables before clustering and do this using R
• Use the elbow method to choose the number of clusters for k-means
• Describe advantages, limitations and assumptions of the kmeans clustering algorithm.

This worksheet covers parts of the Clustering chapter of the online textbook. You should read this chapter before attempting the worksheet.

1. Pokemon¶

We will be working with the Pokemon dataset from Kaggle, which can be found here. This dataset compiles the statistics on 721 Pokemon. The information in this dataset includes Pokemon name, type, health points, attack strength, defensive strength, speed points etc. These are values that apply to a Pokemon's abilities (higher values are better). We are interested in seeing if there are any sub-groups/clusters of pokemon based on these statistics. And if so, how many sub-groups/clusters there are.

Source: https://media.giphy.com/media/3oEduV4SOS9mmmIOkw/giphy.gif

Question 1.0
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Use read_csv to load pokemon.csv from the data/ folder.

Assign your answer to an object called pokemon_full.

Question 1.1
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To start exploring the Pokemon data, create a scatter plot matrix (or pairplot) using ggpairs. The plot should only contain the columns Total to Speed from pm_data. You can check the data wrangling chapter in the textbook to recall how to select a range of columns using select with :.

Assign your answer to an object called pokemon_pairs. Make sure to set a suitable size for the plot.

Question 1.2
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From the pairplot above, it does not look like the pokemon are separated into clear groups in any of the pairwise variable scatterplots. Here, we will continue exploring the relationship between Speed and Defense and see what happens if we try to cluster the data points on these two variables although there are no visually discernable variables in the chart.

First, select the columns Speed and Defense, creating a new dataframe with only those columns.

Assign your answer to an object named pokemon.

Question 1.3
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Next, create a scatter plot of only these two variables so that we can look close at their relationship. Put the Speed variable on the x-axis, and the Defense variable on the y-axis.

Assign your plot to an object called pokemon_scatter. Don't forget to do everything needed to make an effective visualization, including setting an appropriate alpha value of the points.

Question 1.4.1
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The chart above confirms what we saw in the pairplot; there doesn't seem to be visually distinct clusters of points in these two dimensions. Could it still be informative to run clustering with this data? Let's find out by using K-Means to cluster the Pokemon based on their Speed and Defense.

So far when using K-Means, we have scaled our input features. Will it matter much for our clustering if we scale our variables for the pokemon data? Is there any argument against scaling here?

Question 1.4.2
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Now, let's use K-means to cluster the Pokemon based on their Speed and Defense variables.

• Create a recipe named pokemon_recipe that standardizes the data
• Create a model specification named pokemon_spec for K-means clustering with 4 clusters.
• Fit the model using a tidymodels workflow; call the output of the fit() function pokemon_clustering.

Assign your answers to objects called pokemon_recipe, pokemon_spec, and pokemon_clustering.

Note: We set the random seed here because K-means initializes observations to random clusters.

Question 1.5
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Let's visualize the clusters we built in pokemon_clustering. Use the augment function and create a coloured scatter plot of Speed (x-axis) vs Defense (y-axis) with the points coloured by their cluster assignment.

Name this plot pokemon_clustering_plot.

Question 1.6
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Below you can see multiple initializations of k-means with different seeds for K = 4. Can you explain what is happening and how we can mitigate this in the kmeans function?

Question 1.7
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We know that comparing how the WSSD varies for multiple values of $K$ is an important step of selecting a suitable clustering model. That's what we will do next!

For this exercise, you will calculate the total within-cluster sum-of-squared distances for $K$ = 1 to $K$ = 10.

1. Create a tibble with the desired values of $K$.
2. Create a new model specification that sets nstart to 10 and tells k_means you want to tune the number of clusters.
3. Create a new workflow that uses tune_cluster to tune the number of clusters
4. Use the collect_metrics function to collect the results.
5. Use filter, select, and mutate functions to construct a tibble with two columns named num_clusters and total_WSSD. Store that tibble in an object named elbow_stats.

Assign your answer to a tibble object named elbow_stats. It should have the columns num_clusters and total_WSSD.

Question 1.8
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Let's visualize how WSSD changes for as we vary the value of $K$. To do this, create the elbow plot. Put the within-cluster sum of squares on the y-axis, and the number of clusters on the x-axis.

Assign your plot to an object called elbow_plot.

Question 1.9
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Based on the elbow plot above, what value of $K$ would you choose? Explain why.

Question 1.10
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Using the value that you chose for $K$, perform the K-means algorithm, set nstart = 10 and assign your answer to an object called pokemon_final_kmeans.

Augment the data with the final cluster labels and assign your answer to an object called pokemon_final_clusters.

Finally, create a plot called pokemon_final_clusters_plot to visualize the clusters. Include a title, colour the points by the cluster and make sure your axes are human-readable.

Question 1.11
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This looks perhaps a bit better than when we used $K=4$ clusters originally, but is it really a lot better? Use this plot and the elbow plot from Question 1.8 to reason about what might be going on here.

2. Tourism Reviews¶

Source: https://media.giphy.com/media/xUNd9IsOQ4BSZPfnLG/giphy.gif

The Ministry of Land, Infrastructure, Transport and Tourism of Japan is interested in knowing the type of tourists that visit East Asia. They know the majority of their visitors come from this region and would like to stay competitive in the region to keep growing the tourism industry. For this, they have hired us to perform segmentation of the tourists. A dataset from TripAdvisor has been scraped and it's provided to you.

This dataset contains the following variables:

• User ID : Unique user id
• Category 1 : Average user feedback on art galleries
• Category 2 : Average user feedback on dance clubs
• Category 3 : Average user feedback on juice bars
• Category 4 : Average user feedback on restaurants
• Category 5 : Average user feedback on museums
• Category 6 : Average user feedback on resorts
• Category 7 : Average user feedback on parks/picnic spots
• Category 8 : Average user feedback on beaches
• Category 9 : Average user feedback on theaters
• Category 10 : Average user feedback on religious institutions

Question 2.0
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Load the data set from https://archive.ics.uci.edu/ml/machine-learning-databases/00484/tripadvisor_review.csv and clean it so that only the Category # columns are in the data frame (i.e., remove the User ID column).

Assign your answer to an object called clean_reviews.

Question 2.1
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Perform K-means and vary $K$ from 1 to 10 to identify the optimal number of clusters. Use nstart = 100. Assign your answer to a tibble object called tourism_elbow_stats that has the columns num_clusters and total_WSSD.

Afterwards, create an elbow plot to help you choose $K$. Assign your answer to an object called tourism_elbow_plot.

Question 2.2
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From the elbow plot above, which $k$ should you choose? Explain why you chose that $k$.

Question 2.3
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Run K-means again, with the optimal $K$, and assign your answer to an object called reviews_clusters. Use nstart = 100. Then, use the augment function to get the cluster assignments for each point. Name the data frame cluster_assignments.

For the following 2 questions use the following plot as reference.

The visualization below is a density plot, you can think of it as a smoothed version of a histogram. Density plots are more effective for comparing multiple distributions. What we are looking for with these visualizations, is to see which variables have difference distributions between the different clusters.

Question 2.4 Multiple Choice:
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From the plots above, point out the categories that we might hypothesize are driving the clustering? (i.e., are useful to distinguish between the type of tourists?) We list the table of the categories below.

• Category 1 : Average user feedback on art galleries
• Category 2 : Average user feedback on dance clubs
• Category 3 : Average user feedback on juice bars
• Category 4 : Average user feedback on restaurants
• Category 5 : Average user feedback on museums
• Category 6 : Average user feedback on resorts
• Category 7 : Average user feedback on parks/picnic spots
• Category 8 : Average user feedback on beaches
• Category 9 : Average user feedback on theaters
• Category 10 : Average user feedback on religious institutions

A. 10, 3, 5, 6, 7

B. 10, 3, 5, 6, 1

C. 10, 3, 4, 6, 7

D. 10, 2, 5, 6, 7

Assign your answer to an object called answer2.4. Make sure your answer is an uppercase letter and is surrounded by quotation marks (e.g. "F").

Question 2.5
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Discuss one disadvantage of not being able to visualize the clusters when dealing with multidimensional data.